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001451556 001__ 1451556
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001451556 019__ $$a1352975481
001451556 020__ $$a9783031138737$$q(electronic bk.)
001451556 020__ $$a3031138732$$q(electronic bk.)
001451556 020__ $$z3031138724
001451556 020__ $$z9783031138720
001451556 0247_ $$a10.1007/978-3-031-13873-7$$2doi
001451556 035__ $$aSP(OCoLC)1352624707
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001451556 08204 $$a512/.22$$223/eng/20221208
001451556 1001_ $$aCeccherini-Silberstein, Tullio.
001451556 24510 $$aRepresentation theory of finite group extensions :$$bCclifford theory, Mackey obstruction, and the orbit method /$$cTullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli.
001451556 260__ $$aCham, Switzerland :$$bSpringer,$$c2022.
001451556 300__ $$a1 online resource.
001451556 4901_ $$aSpringer Monographs in Mathematics
001451556 504__ $$aIncludes bibliographical references and index.
001451556 5058_ $$a2.5 Some Applications of Mackey Theory to Clifford Theory -- 2.6 The G-Action on the N-Conjugacy Classes -- 2.7 Real, Complex, and Quaternionic Representations and Clifford Theory -- 2.8 Semidirect Products with an Abelian Normal Subgroup -- 2.9 Semidirect Products of Abelian Groups -- 2.10 Representation Theory of Wreath Products of Finite Groups -- 2.11 Multiplicity-Free Normal Subgroups -- 3 Abelian Extensions -- 3.1 The Dual Action -- 3.2 The Conjugation Action -- 3.3 The Intermediary Representations -- 3.4 Diagrammatic Summaries -- 4 The Little Group Method for Abelian Extensions
001451556 5058_ $$a4.1 General Theory -- 4.2 Normal Subgroups with the Prime Condition -- 4.3 Normal Subgroups of Prime Index -- 4.4 The Case of Index Two Subgroups -- 5 Examples and Applications -- 5.1 Representation Theory and Conjugacy Classes of the Symmetric Groups Sn -- 5.2 Conjugacy Classes of An -- 5.3 The Irreducible Representations of An -- 5.4 Ambivalence of the Groups An -- 5.5 An Application to Isaacs' Going Down Theorem -- 5.6 Another Application: Analysis of p2-Extensions -- 5.7 Representation Theory of Finite Metacyclic Groups -- 5.8 Examples: Dihedral and Generalized Quaternion Groups
001451556 5058_ $$a6 Central Extensions and the Orbit Method -- 6.1 Central Extensions -- 6.2 2-Divisible Abelian Groups, Equalized Cocycles, and Schur Multipliers -- 6.3 Lie Rings -- 6.4 The Cocycle Decomposition -- 6.5 The Malcev Correspondence -- 6.6 The Orbit Method -- 6.7 More on the Orbit Method: Induced Representations -- 6.8 More on the Orbit Method: Restricting to a Subgroup -- 6.9 The Orbit Method for the Finite Heisenberg Group -- 6.10 Restricting from Hqt to Hq -- 6.11 The Little Group Method for the Heisenberg Group -- 7 Representations of Finite Group Extensions via Projective Representations
001451556 5058_ $$a7.1 Mackey Obstruction -- 7.2 Unitary Projective Representations -- 7.3 The Dual of a Group Extension -- 7.4 Central Extensions and the Finite Heisenberg Group -- 7.5 Analysis of the Commutant -- 7.6 The Hecke Algebra -- 8 Induced Projective Representations -- 8.1 Basic Theory -- 8.2 Mackey's Theory for Induced Projective Representations -- 9 Clifford Theory for Projective Representations -- 9.1 Preliminaries and Notation -- 9.2 Basic Clifford Theory for Projective Representations -- 9.3 Projective Unitary Representations of a Group Extension
001451556 506__ $$aAccess limited to authorized users.
001451556 520__ $$aThis monograph adopts an operational and functional analytic approach to the following problem: given a short exact sequence (group extension) 1 N G H 1 of finite groups, describe the irreducible representations of G by means of the structure of the group extension. This problem has attracted many mathematicians, including I. Schur, A.H. Clifford, and G. Mackey and, more recently, M. Isaacs, B. Huppert, Y.G. Berkovich & E.M. Zhmud, and J.M.G. Fell & R.S. Doran. The main topics are, on the one hand, Clifford Theory and the Little Group Method (of Mackey and Wigner) for induced representations, and, on the other hand, Kirillovs Orbit Method (for step-2 nilpotent groups of odd order) which establishes a natural and powerful correspondence between Lie rings and nilpotent groups. As an application, a detailed description is given of the representation theory of the alternating groups, of metacyclic, quaternionic, dihedral groups, and of the (finite) Heisenberg group. The Little Group Method may be applied if and only if a suitable unitary 2-cocycle (the Mackey obstruction) is trivial. To overcome this obstacle, (unitary) projective representations are introduced and corresponding Mackey and Clifford theories are developed. The commutant of an induced representation and the relative Hecke algebra is also examined. Finally, there is a comprehensive exposition of the theory of projective representations for finite Abelian groups which is applied to obtain a complete description of the irreducible representations of finite metabelian groups of odd order.
001451556 588__ $$aOnline resource; title from PDF title page (Springer, viewed December 8, 2022).
001451556 650_0 $$aRepresentations of groups.
001451556 650_0 $$aGroup theory.
001451556 655_0 $$aElectronic books.
001451556 7001_ $$aScarabotti, Fabio.
001451556 7001_ $$aTolli, Filippo,$$d1968-
001451556 77608 $$iPrint version: $$z3031138724$$z9783031138720$$w(OCoLC)1334721938
001451556 830_0 $$aSpringer monographs in mathematics.
001451556 852__ $$bebk
001451556 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-13873-7$$zOnline Access$$91397441.1
001451556 909CO $$ooai:library.usi.edu:1451556$$pGLOBAL_SET
001451556 980__ $$aBIB
001451556 980__ $$aEBOOK
001451556 982__ $$aEbook
001451556 983__ $$aOnline
001451556 994__ $$a92$$bISE